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There is no such right triangle.

You have defined the relationship between three sides of a triangle that does not have a 90 degree angle.

In a right triangle the sum of the squares of the shorter sides equals the square of the longest side and 12 + 22 = 5 ; 42 = 16 it does not equal 5

The angles in a triangle with sides 1, 2, 4 units can be found by applying the cosine rule.

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Q: Find the lengths of the side of the right triangle if the longest side of the triangle is four more than the shortest side and the middle side is two more than the shortest side?
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